Discovering Pi

'Give meaning to the existence of Pi by exploring the geometric phenomenon from which it comes'

The enigmatic Pi is a fascination for mathematicians, but it can be a mystery to lots of people. Its decimal places go on forever and and so it is hard to define. It has something to do with circles and there is a button for it on most calculators. Its symbol is a Greek letter but where does it actually come from? How did it come into existence? With this activity, play with the geometry that provides some answers to these questions and discover Pi! See how this helps us derive and use the formula for the circumference of the circle.




Dynamic Geometry is a necessary tool for this investigation, preferably for students but it would be possible with just teacher access. Read below for an outline of the activity or use this  Discovering Pi investigation worksheet and some  follow up work applying the formula for circumference.

Video Starter

This video is just designed to help get the idea of the investigation across quickly

The Investigation

With or without the worksheet the following summarises the investigation. 'Investigate for different regular polygons, the relationship between the perimeter and the longest straight line that fits inside the shape.'


Here follows an outline of the task;

  • Draw a square and the longest diagonal that fits inside it. Divide the perimeter of the square by the length of the diagonal.
  • Repeat for different squares and comment on your findings
  • Repeat for regular hexagons, then Octagons and so on
  • Consider what happens to the appearance of the shape and the result as the number of sides on the shape are increased.
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